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We throw a coin 1 000 000 times. How many times on average will make 13 successful heads? Now the problem with the naive: 1 000 000/(2^13) is that once it made 13 heads the 14 head will happen with 1/2 probability , but it will count as 2 13 successful heads. 15 will happen 4xtimes less, but it will count as 3 13 successful heads. (which is far more probable than 3x1 000 000/(2^13)) if they were happening discretely.So 14 and 15 and anything above will be counted as a 13-success with value of 2,3 and so on. Monte carlo simulation also suggests something is fishy: https://stackoverflow.com/questions...nerator?noredirect=1#comment96559899_54895072 So what exactly is the expected number of 13 successful heads?

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    $\begingroup$ By "successful" do you perhaps mean "successive"? $\endgroup$ – whuber Feb 27 at 12:27
  • $\begingroup$ That is correct $\endgroup$ – Goking Feb 27 at 15:06

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